Max Planck and Albert Einstein's Quantum Theory: Understanding Light and Atomic Structure, Study notes of Chemistry

Download Max Planck and Albert Einstein's Quantum Theory: Understanding Light and Atomic Structure and more Study notes Chemistry in PDF only on Docsity! 1 AuroraBorealis– reallifeatomicexcitement Auroras result from emissions of photons in the upper atmosphere (above 80 km/50 miles), from ionized N2 atoms regaining an electron, and O2 and N2 atoms returning from an excited state to ground state. Particles accelerated from solar winds transfer energy and excited these species; excitation energy is lost by the emission of a photon of light, or by collision with another atom or molecule: • O2emissionsgreenorbrownishͲred • N2emissionsblueorred Topic3:AtomicStructure Learninggoals: • Understandthenatureoflight • Understandthebehaviorof electronsandquantizationofenergy • AtomicLineSpectra • IntroductiontoQuantumMechanics • WaveProperties • QuantumNumbers • AtomicOrbitals • Electronicconfigurationsofatoms Let’sbuildupsome chemistrymuscles. SuggestedProblems(ataminimum):inͲchapterproblems and6.5,6.15,6.17,6.27,6.32,6.33,6.43,6.49,6.55, 6.57,6.63,6.69,6.79,6.85,6.87,6.101,6.103,6.105, 6.113,6.117,6.121, 2 Reminder:ProgrammablecalculatorsareNOTallowedforanyquizorexaminC117!!! YouwillneedanonͲprogrammable(simple)scientificcalculator,withfunctionkeysfor “ex,”“Ln,”“Log,”“10x,”“1/x”(or“xͲ1”),“xy,”andscientificnotation,likeoneofthese: No iPods, iPhones, orcell phones. ElectromagneticSpectrum What’sthecontroversyaboutcellphonefrequencies? Visiblelightisonlyasmallcomponentofthecontinuumofradiant energyknownastheelectromagneticspectrum. 5 ElectromagneticRadiation • Muchofourunderstandingoftheelectronic structureofatomscomesfromanalysisofthelight emitted orabsorbed bysubstances. • Electromagneticradiationoscillateselectricand magneticfieldswhilecarryenergythroughspace. • Electromagneticradiation = Matteremitslightintwoprominentways: 1.)BlackbodySpectra – 2.)EmissionSpectra – Patternsinfrequenciesofabsorption/emission – Continuousspectra – Linespectra TypesofSpectra 6 Blackbodyradiation Emissionmeansthatanobjectiscreatingitsown light— Asthe temperaturegetshotter,thewavelengthofthelightcomingfromthe objectdecreases:Theymovefromredtoblue. BlackbodySpectra=lightemittedbyheatedobjects,dependsprimarily ontemperature IrradiationatRoomTemperature • Aroundroomtemperature,thingsemitinfraͲred light(energywecannotseewithoureyes). • Peopleareroughly100Wlightbulbs,exceptthey emitallinfraredandlongerwavelengthlight. – Totaldailyexpenditure9x106 Joules,or2,000(food) calories. – Normalrateofmetabolismistypically100Ͳ120W – Iflosing>160Wwouldfeelcoldandneedtoincrease activityorcoverwithclothestofeelwarmer. – Duringphysicalactivitythemetabolismismuchhigher andsincetheemissionisnotincreased,theexcessheat iscarriedawaybysweating. Checkout: http://webphysics.davidson.edu/alumni/MiLee/java/bb_mjl.htm 7 Whitelight&continuousspectra Whenradiationfromanylightsourceisseparatedintoits differentwavelengthcomponents,aspectrum isproduced. Continuousspectrum Linespectra • Notallemittedradiationprovidesa continuousspectrumofenergies(colors). • Whendifferentgasesareplacedunder reducedpressure(vacuum)inatubeanda highvoltage(energy)isapplied,thegases emitdifferentcolorsoflight. – NeappearsredͲorange(15distinct lines) – Helooksalmostwhite.Why? – Happearsavividpurple.Why? 10 In1905,AlbertEinsteinusedPlanck’stheory toexplainthephotoelectriceffect. Electronsareejectedfromthesurfaceofa metalexposedtolightofacertainthreshold frequency. Thenumberofelectronsejectedis proportionaltotheintensity. Einsteinproposedthatthebeamoflight= streamofparticles=photons. Eachphoton(oftheincidentlight)must possestheenergygivenbytheequation: QuantumTheory Problemsyoushouldbeabletosolve 1. nknown,calculateʄ 2. ʄ known,calculaten 3. photonenergy(E)known,calculatenand/orʄ 4. ʄ ornknown,calculateEforonephoton 5. ʄ ornknown,calculateEforamoleofphotons Seekhelpatdiscussionandofficehoursifyouareunsure thatyouaredoingtheseproblemscorrectly. ʄʆ =c E=hʆ E=hc/ʄ h=6.626x10Ͳ34 J•s 11 Howdoesallthisrelatetodailylife? Visiblelightdoesn’thurttheskin(evenlotsofit).UVlightdoes. HowdoesdamagerelatetotheenergyoftheUVlight? PABA, pͲaminobenzoic acid, was widely used in sunscreens as a UV filter. It is a UVB absorber, meaning that it can absorb wavelengths between 290Ͳ320 nm. Calculate the amount of energy (in kJ/mol) that it is absorbed assuming 313 nm. TheRydbergequationcanbeusedtocalculatethewavelengthsofthefour visiblelinesintheemissionspectrumofhydrogen. • Rь istheRydbergconstant(1.09737317x107 mо1) • ʄ thewavelengthofalineinthespectrum,n1 andn2 arepositive integerswheren1 >n2. NeilsBohrattributedtheemissionofradiationbyanenergizedhydrogenatom totheelectrondroppingfromahigherͲenergyorbittoalowerone. • En istheenergy • n isapositiveinteger • n =ьandEь =0 BohrTheory 2 2 1 2 1 1 1 = R n nO f § · ¨ ¸ © ¹ 12 Forhydrogen,thelowestenergy(moststable)stateoccurswhenn =1. BohrTheory • Thelowestenergystateiscalledthe . • Thestabilityoftheelectrondecreasesasn increases. • Eachenergystateinwhichn>1iscalledan . • Duringanemission,anelectrondropsfrom anexcitedstatetoalowerenergystate. • nf isthefinalstate • ni istheinitialstate 18 2 2 f i 1 1 = = 2.18 10 JE h n n Q  § · '  u ¨ ¸ © ¹ 18 2 1 = 2.18 10 JnE n  § · u ¨ ¸ © ¹ LouisdeBrogliereasonedthatiflightcanbehavelikea streamofparticles(photons),thenelectronscouldexhibit wavelikeproperties. (1892– 1987) 1929NobelPrizeinPhysics AccordingtodeBroglie, electronsbehavelike standingwaves. Onlycertainwavelengths areallowed. Ata ,the amplitudeofthewaveis zero. WavePropertiesofMatter ʄisthewavelength;m isthemass (inkg);u isthevelocity(inm/s) 15 Theprincipalquantumnumber(n)designatesthesize oftheorbital. • Mustbeintegers(1,2,3,etc.) • Largervaluesofn correspondtolargerorbitals. • Oftenreferredtoasshells • Alignswiththeperiodintheperiodictable Theangularmomentquantumnumber(l)describestheshape oftheorbital. • Thevaluesofl areintegersthatdependonthevalueofn. • Theallowedvaluesofl rangefrom0to n– 1. • l isreferredtoasa . QuantumNumbers l 0 1 2 3 Orbital designation Themagneticquantumnumber(ml)describesthe oftheorbitalinspace. Thevaluesofml areintegersthatdependonthevalueoftheangular momentquantumnumber: – l,…0,…+l QuantumNumbers 16 Theelectronspinquantumnumber (ms)isusedto specifyan . Therearetwopossibledirectionsofspin. Allowedvaluesofms are . QuantumNumbers Tosummarizequantumnumbers: principal(n)size angular(l)shape magnetic(ml)orientation electronspin(ms)directionofspin Requiredtodescribeanatomicorbital Requiredtodescribeanelectroninan atomicorbital 2px …andthecliffnotesversion… 17 WhichofthefollowingsetsofQNisnotpossible? (a)? (b)? (c) ? Quantum number (a) (b) (c) Principal (n) 1 2 3 Angular moment (l) 1 0 2 Magnetic (ml) 0 0 –2 Electron spin (ms) +½ +½ –½ QuantumNumbers Allsorbitals aresphericalinshapebutdifferinsize: 1s <2s <3s 2s AtomicOrbitals 20 Howdoesthisrelatetotheperiodictable? The describeshowtheelectronsare distributedinthevariousatomicorbitals. Inagroundstate hydrogenatom,theelectronisfoundinthe1s orbital. 1s1 1s 2s 2p 2p 2p En er gy Theuseofanuparrowindicatesandelectronwith ms =+½ Groundstateelectron configurationofhydrogen ElectronicConfigurations 21 Ifanelectronisfoundinahigherenergyorbitalthanthelowestempty orbital,theatomisinan . 2s1 1s 2s 2p 2p 2p En er gy Apossibleexcitedstateelectron configurationofhydrogen ElectronicConfigurations Accordingtothe ,no twoelectronscanhavethesamefourquantumnumbers. 1s2 1s 2s 2p 2p 2p En er gy Thegroundstateelectron configurationofhelium Quantum number Principal (n) Angular moment (l) Magnetic (ml) Electron spin (ms) 1 0 0 + ½ 1 0 0 വ ½ ElectronicConfigurations 22 The statesthatelectronsare addedtothelowestenergyorbitalsfirstaddingtothenexthigherenergy orbitals(groundstateconfiguration). 1s22s1 1s 2s 2p 2p 2p En er gy Thegroundstateelectron configurationofLi ElectronicConfigurations Accordingto , themoststablearrangement ofelectronsistheoneinwhichthenumberofelectronswiththesamespin ismaximized. 1s22s22p2 1s 2s 2p 2p 2p En er gy Thegroundstateelectron configurationofC The2p orbitalsare . Put1electronineachdegenerateorbitalbeforepairing(Hund’s rule). ElectronicConfigurations